论文标题
顶点张量类别的直接限制完成
Direct limit completions of vertex tensor categories
论文作者
论文摘要
我们表明，在所有已知的Virasoro和Aggine Lie代数张量类别的条件下，顶点张量类别的直接限制完成继承了顶点和编织的张量类别结构。结果是顶点操作员（超级）代数扩展理论也适用于无限阶扩展。作为一个应用程序，我们将某些模块的刚性和非分级顶点张量类别与$ \ mathfrak {osp}（1 | 2）$和$ n = 1 $ super virasoro代数的offine顶点超级抗体类别相关联，均与Virasoro Algebra模块的类别相关联。
We show that direct limit completions of vertex tensor categories inherit vertex and braided tensor category structures, under conditions that hold for example for all known Virasoro and affine Lie algebra tensor categories. A consequence is that the theory of vertex operator (super)algebra extensions also applies to infinite-order extensions. As an application, we relate rigid and non-degenerate vertex tensor categories of certain modules for both the affine vertex superalgebra of $\mathfrak{osp}(1|2)$ and the $N=1$ super Virasoro algebra to categories of Virasoro algebra modules via certain cosets.
